CN110069866A - A kind of design of pressure vessels method based on Swarm Intelligence Algorithm - Google Patents
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Abstract
The design of pressure vessels method based on Swarm Intelligence Algorithm that the present invention relates to a kind of improves the design problem that locust algorithm and optimization pressure container cost minimize using Gaussian mutation and chaology.Design of pressure vessels problem can be abstracted into 4 structural parameters, and the mathematical model of 4 constraint conditions and 1 objective function is used for the optimization design of algorithm.Can be seen that algorithm proposed by the invention (GC-GOA) from the data of design can preferably design the lesser pressure vessel of cost.
Description
Technical field
The present invention relates to design of pressure vessels field, especially a kind of design of pressure vessels side based on Swarm Intelligence Algorithm
Method.
Background technique
For the design problem of pressure vessel cost minimization, this belongs to, and a kind of there are the Non-Linear Programmings of multi-constraint condition
Problem.Relative to the tentative calculation mode in engineering, has gravitation search algorithm (Gravitational Search
Algorithm, GSA), evolution strategy algorithm (Evolutionary Strategies, ES), genetic algorithm (Genetic
Algorithm, GA) it is used for optimization pressure Vessel Design problem, but design effect need to be improved.
Locust algorithm (Grasshopper Optimization Algorithm, GOA) is by Australian team-
A kind of novel swarm intelligence algorithm that Shahrzad Saremi et al. was proposed in 2017, this algorithm is in Solve problems optimization
It is with good performance, but it is there are still precocious phenomenon, the problems such as being easily trapped into local optimum.
Summary of the invention
In view of this, the purpose of the present invention is to propose to a kind of design of pressure vessels method based on Swarm Intelligence Algorithm, is adopted
With the locust algorithm after optimization come the design problem of pressure container, the cost that can preferably optimize pressure vessel is set
Meter.
The present invention is realized using following scheme: a kind of design of pressure vessels method based on Swarm Intelligence Algorithm, including with
Lower step:
Step S1: by the mathematical model of pressure vessel is defined as:Wherein
Pressure vessel is the cylindrical chamber for including two hemispherical heads, X1To X4For four variables, T is the thickness of the shell of cylindrical chamber, S
The thickness of hemispherical head, R are the inside radius of hemispherical head, and L is the length of cylindrical chamber；If objective function are as follows:
Step S2: carrying out initialization of population, i.e. the initial value of four variables in initialization step S1 obtains the column of N row four
Space of the matrix as solution, wherein N is population quantity；
Step S3: while the position of locust individual is updated using following two formula:
In formula,It is i-th of locust individual in the position that d is tieed up, i belongs to (1,2 ..., N), corresponding i-th of the population of i；
D is dimension, d=4；XiThe solution of one group of four-dimension array that is found of corresponding i-th of the population in position；ubd、lbdRespectively indicate d dimension
The upper limit of search space, lower limit, the range of variables of search space range corresponding pressure Vessel Design problem here；C is adaptive
Coefficient is answered, s is action intensity；dijFor the distance between ith and jth locust, i.e. dij=| xj-xi|,Table respectively
Show ith and jth locust individual in the position that d is tieed up (annotation: capitalizationWith small letterMean it is the same, can be with
Think capitalizationIt is small letterIt is primary according to formula again assignment；It is only small letter but when most startingIt is logical
Cross grasshopper nearbyAttraction Degree influence generate capitalizationCapitalizationAllow for neighbouring grasshopper influences i-th
A locust individual is in the position that d is tieed up)；It is the optimal location that has found at present, i.e., corresponding to current minimal design cost
The solution of four variables；Indicate position of i-th of individual in the t times iteration, r1For the random number of section (- 1,1)；G is full
Random number of the sufficient Gaussian Profile in (0,1) range；r2For the random number of section (0,0.7)；Initial matrix Zn-1By
The new matrix Z with Chaotic Behavior obtained after logistic chaos operatorn,Indicate i-th of individual in t iteration most
Excellent position；
Step S4: whether the range for checking solution is more than range of variables, and updates adaptation coefficient c, calculating target function；
Step S5: judging whether to have traversed current population, if it is not, return step S3 is repeated, if having traversed current population, into
Enter step S6；
Step S6: judging whether current iteration number is less than maximum number of iterations, if so, return step S3, otherwise defeated
The minimum value of objective function out, the minimal design cost as pressure vessel.
Further, in step S1, the constraint condition of the mathematical model of the pressure vessel are as follows:
Further, in step S1, the range of variables of the mathematical model of the pressure vessel are as follows: 0≤X1,X2≤99,10≤
X3,X4≤200。
Further, in step S2, using Sinusoidal chaotic maps initialization population, such as following formula:
In formula, a takes 2.3, initial matrix ykThe new square with Chaotic Behavior is obtained after Sinusoidal chaos operator
Battle array yk+1。
Further, in step S4, the update of adaptation coefficient c uses following formula:
In formula, cmax、cminThe respectively maximum value and minimum value of adaptation coefficient；T indicates current the number of iterations；tmax
Indicate maximum number of iterations.
Further, in step S3, the update of action intensity s uses following formula:
In formula, f indicates attraction intensity；L indicates attractive length range.
Compared with prior art, the invention has the following beneficial effects: the present invention is low for locust algorithmic statement precision, is easy
In place of the deficiencies of falling into local optimum, proposes a kind of Gaussian mutation and chaology combines the locust algorithm of optimization.For
The design of pressure vessels performance deficiency of existing algorithm at present, the invention proposes Gaussian mutations and chaology to improve locust algorithm
And the Cost Design problem of optimization pressure container, it can preferably design the lesser pressure vessel of cost.
Detailed description of the invention
Fig. 1 is the design of pressure vessels schematic diagram of the embodiment of the present invention.
Specific embodiment
The present invention will be further described with reference to the accompanying drawings and embodiments.
It is noted that described further below be all exemplary, it is intended to provide further instruction to the application.Unless another
It indicates, all technical and scientific terms used herein has usual with the application person of an ordinary skill in the technical field
The identical meanings of understanding.
It should be noted that term used herein above is merely to describe specific embodiment, and be not intended to restricted root
According to the illustrative embodiments of the application.As used herein, unless the context clearly indicates otherwise, otherwise singular
Also it is intended to include plural form, additionally, it should be understood that, when in the present specification using term "comprising" and/or " packet
Include " when, indicate existing characteristics, step, operation, device, component and/or their combination.
As shown in Figure 1, a kind of design of pressure vessels method based on Swarm Intelligence Algorithm is present embodiments provided, including with
Lower step:
Step S1: by the mathematical model of pressure vessel is defined as:Wherein
Pressure vessel is the cylindrical chamber for including two hemispherical heads, X1To X4For four variables, T is the thickness of the shell of cylindrical chamber, S
The thickness of hemispherical head, R are the inside radius of hemispherical head, and L is the length of cylindrical chamber；If objective function are as follows:
Step S2: carrying out initialization of population, i.e. the initial value of four variables in initialization step S1 obtains the column of N row four
Space of the matrix as solution, wherein N is population quantity；
Step S3: while the position of locust individual is updated using following two formula:
Wherein, former locust algorithm using above formula to grasshopper carry out location updating, but its be easily trapped into local optimum and can not
Globally optimal solution is obtained, therefore the present embodiment combination Gaussian mutation and logistic chaos make improvements, formula is as follows:
In formula,It is i-th of locust individual in the position that d is tieed up, i belongs to (1,2 ..., N), corresponding i-th of the population of i；
D is dimension, d=4；XiThe solution of one group of four-dimension array that is found of corresponding i-th of the population in position；ubd、lbdRespectively indicate d dimension
The upper limit of search space, lower limit, the range of variables of search space range corresponding pressure Vessel Design problem here；C is adaptive
Coefficient is answered, s is action intensity；dijFor the distance between ith and jth locust, i.e. dij=| xj-xi|,Table respectively
Show ith and jth locust individual in the position that d is tieed up (annotation: capitalizationWith small letterMean it is the same, can be with
Think capitalizationIt is small letterIt is primary according to formula again assignment；It is only small letter but when most startingIt is logical
Cross grasshopper nearbyAttraction Degree influence generate capitalizationCapitalizationAllow for neighbouring grasshopper influences i-th
A locust individual is in the position that d is tieed up)；It is the optimal location that has found at present, i.e., corresponding to current minimal design cost
The solution of four variables；Indicate position of i-th of individual in the t times iteration, r1For the random number of section (- 1,1)；G is full
Random number of the sufficient Gaussian Profile in (0,1) range；r2For the random number of section (0,0.7)；Initial matrix Zn-1By
The new matrix Z with Chaotic Behavior obtained after logistic chaos operatorn,Indicate i-th of individual in t iteration most
Excellent position；The initial value Z of Z matrixn-1Any value in section (0,1) except 0.25,0.5,0.75 is taken, and mixed according to logistic
Ignorant mapping generates one group of chaos sequence, wherein the sequence is in Complete Chaos state when μ takes 4.
Step S4: whether the range for checking solution is more than range of variables, and updates adaptation coefficient c, calculating target function；
Step S5: judging whether to have traversed current population, if it is not, return step S3 is repeated, if having traversed current population, into
Enter step S6；
Step S6: judging whether current iteration number is less than maximum number of iterations, if so, return step S3, otherwise defeated
The minimum value of objective function out, the minimal design cost as pressure vessel.
In the present embodiment, in step S1, the constraint condition of the mathematical model of the pressure vessel are as follows:
In the present embodiment, in step S1, the range of variables of the mathematical model of the pressure vessel are as follows: 0≤X1,X2≤99,
10≤X3,X4≤200。
Preferably, in this embodiment, the initialization of population of GC-GOA algorithm corresponds to the thickness of the shell (T) of cylindrical chamber, half
The thickness (S) of dome head, the inside radius (R) of hemispherical head, this four variables of the length (L) of cylindrical chamber are in each independent variable
N group initial value in range, i.e. initial position.N refers to that population quantity, N group feasible solution in corresponding background problems, one group of feasible solution are
Four-dimensional array, so the space entirely solved is the matrix that N row four arranges.
In the present embodiment, original locust algorithm is randomly generated the initial solution of population, the diversity of such primary data
Difference.The present embodiment uses Sinusoidal chaotic maps initialization population, and the effect of chaos is the more of increase data initial distribution
Sample, specifically, in step S2, using Sinusoidal chaotic maps initialization population, such as following formula:
In formula, a takes 2.3, and being initialized using the chaos to population can make locust initial position be more evenly distributed, and reduces
Population falls into the probability of local optimum.Initial matrix ykIt is obtained after Sinusoidal chaos operator new with Chaotic Behavior
Matrix yk+1。
In the present embodiment, in step S4, the update of adaptation coefficient c uses following formula:
In formula, cmax、cminThe respectively maximum value and minimum value of adaptation coefficient；T indicates current the number of iterations；tmax
Indicate maximum number of iterations.
In the present embodiment, in step S3, the update of action intensity s uses following formula:
In formula, f indicates attraction intensity；L indicates attractive length range.
In the present embodiment, the pseudocode of the present embodiment algorithm is as follows:
The present embodiment by improved locust algorithm (GC-GOA) carry out pressure vessel relatively minimal Cost Design, and with draw
Power searching algorithm (GSA), evolution strategy algorithm (ES), genetic algorithm (GA), original locust algorithm (GOA) are designed effect
Comparison, data result is as shown in table 1.Purpose is to minimize objective function, that is, designs the pressure vessel of minimum cost.
The parameter of program is set as population 60, maximum number of iterations 500, and program reruns 30 times, and output result is such as
Shown in following table.
As can be known from the above table, GC-GOA by optimization thickness of the shell (T), the thickness (S) of hemispherical head, hemispherical head it is interior
Radius (R), this four major influence factors of the length (L) of cylindrical chamber, it is lesser finally to calculate relatively other four algorithms
Cost result.The sequence of design data is respectively GSA maximum, followed by GOA, ES, GA, and relatively minimal is the present embodiment
GC-GOA.This illustrates that the method for the present embodiment optimizes the Cost Design of pressure vessel better.
The present embodiment using Gaussian mutation and chaology improves locust algorithm and optimization pressure container cost minimizes
Design problem.Design of pressure vessels problem can be abstracted into 4 structural parameters, the mathematics of 4 constraint condition and 1 objective function
Model is used for the optimization design of algorithm.Can be seen that proposed algorithm (GC-GOA) from the data of design can preferably set
Count out the lesser pressure vessel of cost.It is low for locust algorithmic statement precision, the deficiencies of being easily trapped into local optimum place, this reality
Apply the locust algorithm that example proposes a kind of Gaussian mutation and chaology combines optimization.Hold for having the pressure of algorithm at present
Device design performance defect, the present embodiment propose Gaussian mutation and chaology improve locust algorithm and optimization pressure container at
The design problem.
It should be understood by those skilled in the art that, embodiments herein can provide as method, system or computer program
Product.Therefore, complete hardware embodiment, complete software embodiment or reality combining software and hardware aspects can be used in the application
Apply the form of example.Moreover, it wherein includes the computer of computer usable program code that the application, which can be used in one or more,
The computer program implemented in usable storage medium (including but not limited to magnetic disk storage, CD-ROM, optical memory etc.) produces
The form of product.
The application is referring to method, the process of equipment (system) and computer program product according to the embodiment of the present application
Figure and/or block diagram describe.It should be understood that every one stream in flowchart and/or the block diagram can be realized by computer program instructions
The combination of process and/or box in journey and/or box and flowchart and/or the block diagram.It can provide these computer programs
Instruct the processor of general purpose computer, special purpose computer, Embedded Processor or other programmable data processing devices to produce
A raw machine, so that being generated by the instruction that computer or the processor of other programmable data processing devices execute for real
The device for the function of being specified in present one or more flows of the flowchart and/or one or more blocks of the block diagram.
These computer program instructions, which may also be stored in, is able to guide computer or other programmable data processing devices with spy
Determine in the computer-readable memory that mode works, so that it includes referring to that instruction stored in the computer readable memory, which generates,
Enable the manufacture of device, the command device realize in one box of one or more flows of the flowchart and/or block diagram or
The function of being specified in multiple boxes.
These computer program instructions also can be loaded onto a computer or other programmable data processing device, so that counting
Series of operation steps are executed on calculation machine or other programmable devices to generate computer implemented processing, thus in computer or
The instruction executed on other programmable devices is provided for realizing in one or more flows of the flowchart and/or block diagram one
The step of function of being specified in a box or multiple boxes.
The above described is only a preferred embodiment of the present invention, being not that the invention has other forms of limitations, appoint
What those skilled in the art changed or be modified as possibly also with the technology contents of the disclosure above equivalent variations etc.
Imitate embodiment.But without departing from the technical solutions of the present invention, according to the technical essence of the invention to above embodiments institute
Any simple modification, equivalent variations and the remodeling made, still fall within the protection scope of technical solution of the present invention.
Claims (6)
1. a kind of design of pressure vessels method based on Swarm Intelligence Algorithm, it is characterised in that: the following steps are included:
Step S1: by the mathematical model of pressure vessel is defined as:Wherein pressure
Container is the cylindrical chamber for including two hemispherical heads, X1To X4For four variables, T is the thickness of the shell of cylindrical chamber, S hemisphere
The thickness of shape end socket, R are the inside radius of hemispherical head, and L is the length of cylindrical chamber；If objective function are as follows:
Step S2: carrying out initialization of population, i.e. the initial value of four variables in initialization step S1 obtains the matrix of the column of N row four
As the space of solution, wherein N is population quantity；
Step S3: while the position of locust individual is updated using following two formula:
In formula,It is i-th of locust individual in the position that d is tieed up, i belongs to (1,2 ..., N), corresponding i-th of the population of i；D is
Dimension, d=4；XiThe solution of one group of four-dimension array that is found of corresponding i-th of the population in position；ubd、lbdRespectively indicate d dimension search
The upper limit in space, lower limit, the range of variables of search space range corresponding pressure Vessel Design problem here；C is adaptive system
Number, s is action intensity；dijFor the distance between ith and jth locust, i.e. dij=| xj-xi|；It is to have found most at present
Excellent position, i.e., the solution of four variables corresponding to current minimal design cost；Indicate i-th of individual in the t times iteration
Position, r1For the random number of section (- 1,1)；G is the random number for meeting Gaussian Profile in (0,1) range；r2For section (0,
0.7) random number；Initial matrix Zn-1The new matrix Z with Chaotic Behavior obtained after logistic chaos operatorn,
Indicate optimal location of i-th of individual in t iteration；
Step S4: whether the range for checking solution is more than range of variables, and updates adaptation coefficient c, calculating target function；
Step S5: judging whether to have traversed current population, if it is not, return step S3 is repeated, if having traversed current population, into step
Rapid S6；
Step S6: judging whether current iteration number is less than maximum number of iterations, if so, return step S3, otherwise exports mesh
The minimum value of scalar functions, the minimal design cost as pressure vessel.
2. a kind of design of pressure vessels method based on Swarm Intelligence Algorithm according to claim 1, it is characterised in that: step
In rapid S1, the constraint condition of the mathematical model of the pressure vessel are as follows:
3. a kind of design of pressure vessels method based on Swarm Intelligence Algorithm according to claim 1, it is characterised in that: step
In rapid S1, the range of variables of the mathematical model of the pressure vessel are as follows: 0≤X1,X2≤99,10≤X3,X4≤200。
4. a kind of design of pressure vessels method based on Swarm Intelligence Algorithm according to claim 1, it is characterised in that: step
In rapid S2, using Sinusoidal chaotic maps initialization population, such as following formula:
In formula, a takes 2.3, initial matrix ykThe new matrix y with Chaotic Behavior is obtained after Sinusoidal chaos operatork+1。
5. a kind of design of pressure vessels method based on Swarm Intelligence Algorithm according to claim 1, it is characterised in that: step
In rapid S4, the update of adaptation coefficient c uses following formula:
In formula, cmax、cminThe respectively maximum value and minimum value of adaptation coefficient；T indicates current the number of iterations；tmaxIt indicates
Maximum number of iterations.
6. a kind of design of pressure vessels method based on Swarm Intelligence Algorithm according to claim 1, it is characterised in that: step
In rapid S3, the update of action intensity s uses following formula:
In formula, f indicates attraction intensity；L indicates attractive length range.
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| US20120005138A1 (en) * | 2010-06-30 | 2012-01-05 | International Business Machines Corporation | Modifying constraint-compliant populations in population-based optimization |
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